A commonly used resource for outdoor navigation is satellite positioning technology, otherwise known as a Global Navigation Satellite System (GNSS). One example of a fully operational GNSS is the United States NAVSTAR Global Positioning System (GPS)—which will be referred to below when generally discussing satellite positioning technology. However, it will be appreciated that satellite positioning technologies other than GPS may be used in its place.
The operation of GPS is well known in the art, and generally employs a GPS receiver arranged to receive signals from a number of GPS satellites. Each satellite broadcasts its own location and providing the GPS receiver can receive the broadcasted signals from a sufficient number and distribution of satellites, the GPS receiver can infer its own position.
An entity wanting to self-localise may therefore employ a positioning system having a GPS receiver. However, in the event that a GPS receiver is not able to infer its position—for example due to signal interference, then it may be possible for the positioning system to make use of other positioning resources.
For example, a navigation system can navigate using radio signals transmitted by terrestrial radio transmitters such as cellular telephone base stations, television and the like. The signals transmitted by such radio transmitters have distinguishing radio signal characteristics—such as repeated and unique code words—that can be exploited by a suitable positioning system for navigation. These radio signal characteristics along with information about the location the transmitters can be used to determine the position of an entity using known localisation techniques such as multilateration and Enhanced Observed Time Difference (EOTD) as is known in the art.
The regular or otherwise predictably repeated code words are used to allow the receiver of those signals to synchronise with the transmitter. Once synchronised with a set of transmitters, a receiver can therefore determine the relative arrival times of the code words from the available set. As the receiver moves and this set of relative times varies, the receiver can determine its position accordingly. This process is relatively straightforward for transmitters that are synchronised with one another (as is the case with GPS).
However, terrestrial radio signal transmitters that are available to a receiver are not usually synchronised—even if they are set up to transmit the same radio signal type, with the same code word repeat rate. For radio signal transmitters of different types (e.g. different bandwidths and/or frequencies)—e.g. a cellular transmitter versus a DAB transmitter—synchronisation is highly improbable.
As can be observed from a navigation system such a GPS, synchronisation between the radio signal sources is very useful for radio localisation—but is often not possible in an environment in which opportunistic unsynchronised terrestrial radio signals are the only radio signal sources available for localisation.
One known solution in the art is to compensate for the lack of synchronisation by calculating clock offsets (relative to an imaginary universal ‘absolute’ clock) for each transmitter and storing these values for use as clock corrections. In particular, a navigation system can make use of the following Equation 1 to calculate transmitter clock offsets for use in ‘emulating’ synchronicity:ct=|r−b|+ε+α  Equation 1
where:
c is the known speed of the radio waves;
t represents the arrival time (measured at the receiver position using a clock local to the mobile receiver) of a transmission from a transmitter;
r and b are vectors of the positions of the receiver and transmitter respectively. For example, each vector could be the “x, y” values in an 2D Cartesian environment;
ε represents the error of the clock local to the mobile receiver, and;
α represents the transmitter clock offset.
Prior art navigations systems that attempt to make use of unsynchronised radio transmitters for navigation can therefore calculate the transmitter clock offset a and local clock error ε via the mobile receiver collecting timing measurements at a number of different known mobile receiver positions relative to a stationary transmitter having a known location.
However, the calculation of the transmitter clock offset a and local clock error ε values can be computationally expensive, especially when considering that multiple transmitters are required for effective self-localisation. This is especially the case in a system that has the capability of dealing with imperfect data (for example by applying a localisation estimation filter). In such a case, a state vector will need to be maintained including and calculating the offset values for every transmitter, and the errors/uncertainties associated with them.
Furthermore, if a relatively cheap and simple navigation device is employed, the local onboard clock is not likely to be stable. Therefore, the calculated value of a local clock error at one instance does not necessarily apply at another instance, adversely affecting the position calculation. Therefore, it would be beneficial to negate the effect of local clock error.
Whilst it is possible to obtain a highly stable clock reference using atomic clock references, or via a GPS fix, these are not necessarily practical solutions. Atomic clock references are heavy, expensive and unsuitable for a portable navigation device. A stable timing reference can be obtained via GPS, but this relies on a continuous GPS fix, and so is not possible under conditions in which a GPS signal cannot be obtained.
It is possible to formulate a local clock error model with which an attempt can be made to compensate for the likely error in an unstable local clock. However, the model needs to be calculated/calibrated for the eccentricities of each local clock independently and updated over time. To do this is computationally expensive, and so undesirable in a portable system in which processing power and battery life are valuable resources.
These are problems associated with the prior art devices that make use of the above Equation 1. Accordingly, it may be desirable to provide a relatively cheap, portable navigation device able to utilise terrestrial radio signal transmitters for self-localisation in the event that a GPS signal cannot be obtained. To save on battery usage and overall weight, it may also be desirable to reduce the computational burden involved with self-localisation of such a device beyond those making use of the above Equation 1.